When Does Forced Idle Time Improve Performance in Polling Models?
针对穷尽服务和门控服务两种轮询模型，给出了明确公式，说明当平均总设置时间低于某个临界值时，强制服务器空闲固定时长可降低期望等待时间，并给出了对称模型下的显式公式。
Sarkar and Zangwill (1991) showed by numerical examples that reduction in setup times can, surprisingly, actually increase work in process in some cyclic production systems (that is, reduction in switchover times can increase waiting times in some polling models). We present, for polling models with exhaustive and gated service disciplines, some explicit formulas that provide additional insight and characterization of this anomaly. More specifically, we show that, for both of these models, there exist simple formulas that define for each queue a critical value z* of the mean total setup time z per cycle such that, if z z*, then the expected waiting time at that queue will be minimized if the server is forced to idle for a constant length of time z* − z every cycle; also, for the symmetric polling model, we give a simple explicit formula for the expected waiting time and the critical value z* that minimizes it.